When the Queen turned 80 the palace published 80 facts about her life and reign. Fact #38 read (copied from the Monarchy's website):
38. The Queen has sat for 139 official portraits during her lifetime, two of which were with The Duke of Edinburgh. The most recent sitting was for Rolf Harris (2005). Her Majesty was just seven years old when she sat for her first portrait in 1933, which was commissioned by her mother and painted by the Hungarian artist Philip Alexius de László.
I imagine there have been at least a dozen or more in the years since.